Course for international guest/part time students

Faculty

Faculty of Primary and Pre-school Education

Organization

TÓK Department of Mathematics

Code

ERA12E

Title

Ball Geometry

Usual semester

Spring

Published semester

2025/26/2

ECTS

4

Language

en

Learning outcomes

Ball geometry Improve your understanding of the concepts of plane and solid geometry, your way of thinking and your orientation in them understanding. CONTENT OF THE SUBJECT: The development of the early formation of geometrical concepts with the help of spherical or spheroidal bodies such as fruits, balls, spherical construction tools, etc. Remarks on continuing the topic in higher grades. Freehand drawing and geometric constructions on spherical surfaces. Spherical games on 3D models and on the computer screen. Gaining practical experience in primary school. The relevant methodology of dealing with young children.

Course content

KNOWLEDGE The student - develops spatial perception; - learns the basis and possible modelling of non-Euclidean geometries; - deepen mathematical knowledge through the representation of geometric concepts in a variety of geometries; - defines and constructs the mathematical concepts represented in multiple geometric models. CONTACT The student - be proficient in the use of the drawing sphere; - a deeper knowledge and understanding of both inductive and deductive ways of constructing mathematics; - develops constructive and problem-solving skills. ATTITUDE The student - represents that mathematical concepts cannot have only one structure; - understands and sees that mathematics is also a human construction, in which the creative mind has freedom; - represents that the comparative method helps students to understand the true meaning of mathematics the true nature of mathematics and to understand mathematical concepts more deeply. AUTONOMY RESPONSIBILITY The student recognises and accepts that the structure of mathematics is not monolithic and that mathematics is is not an isolated discipline.

Assessment method

We don't write test papers during the semester. Before the exam session begins, I'll send you a summary of what we've accomplished on 15-20 topics and 15-20 unsolved problems. The exam is conducted entirely online, in the form of a written test. You choose one topic and three problems from the list, write an essay on the selected topic of 2-3 pages, and try to solve the three selected problems. I don't expect complete solutions, only that you demonstrate the ability to think outside the Euclidean framework.

Bibliography

Required literature Lénárt, I.: Alternative models on the drawing ball. In: Educational Studies in Mathematics, 24/3 pp.277-312 1993. The Plane-Sphere Project. Mathematics Teaching, MT 187, pp. 22-26, England, 2004. Paper Geometry Vs Orange Geometry - Comparative Geometry on the Plane and the Sphere. Mathematical Association of Victoria. Annual Conference 2009. La Trobe University, Bundoora Australia. http://www.mav.vic.edu.au/files/conferences/2009/21Lenart.pdf Lénárt, I.: Adventures on the Lénárt Sphere. Blackline masters for the middle and high school. Key Curriculum Press, Berkeley, California (1996).

Programmes of the course